This phase II clinical trial will test the efficacy of anti-CD3 x anti-Her2/neu bispecific antibody (Her2Bi) armed activated T cells (aATC) immunotherapy following neoadjuvant chemotherapy (chemoT) in women with triple negative (TNBC) operable breast cancer (BrCa) who do not achieve a complete pathologic response (pCR) after neoadjuvant chemoT. TNBC are tumors that are estrogen receptor, progesterone receptor, and Her2/neu (0-2+ by immunohistochemistry) negative. Less than 25% of all patients with TNBC treated with chemoT achieve pCR at surgery. Women with TNBC who do not achieve a pCR after preoperative chemoT, have a much poorer prognosis compared to those who achieve a pCR. New strategies are needed to target these tumors with a very low levels of Her2/neu expression (0-2+). This phase II trial combines anthracycline/taxane-based neoadjuvant chemoT with 4 infusions of aATC to determine whether this combination increases pathological complete responses (pCR) and recurrence free survival. The use of aATC in extremely low Her2/neu expressing tumors is supported by phase I clinical and immunologic data in women with HER2 0-2+ status. ChemoT prior to immunotherapy (IT) will deplete lymphocytes and regulatory cells to optimize T cell expansion and vaccination with in situ tumor lysates resulting from chemoT and IT. The first aim is to determine in a phase II clinical trial of women with stage II-III TNBC if a neoadjuvant chemoT followed by IT improves the pCR rate at the time of surgery and to investigate the association between pCR and clinical responses (DFS and OS). IT will consist of 20 x 109 aATC given once per week for 4 weeks. The second aim is to determine if aATC will modulate the anti-tumor activity in the blood and tumor and to determine if there is an association between systemic and tumor site immune responses. The third aim is to determine if aATC decreases the frequency of putative CD44hi/CD24lo, CD133+, ALDH1 positive breast cancer stem cells (CSC) in the tumor tissue at the time of surgery compared to that found in the tumor biopsy specimen after chemoT and whether such changes in CSC correlate with clinical responses observed in Aim 1. Immune monitoring will occur pre-IT, prior to infusion #3 (midpoint of IT), after IT and prior to surgery, and 1 month after surgery. If this approach induces anti-tumor immunity that clears CSC at the tumor sites and induces long-term anti-tumor immunity, pCRs will increase and recurrence rates will decrease. Such results will be have an extraordinarily high impact for women with TNBC and provide a paradigm shift for use of IT with neoadjuvant chemoT in women with TNBC. Furthermore, this strategy could be applied to a number of solid tumors and hematologic malignancies.